IB Mathematics Applications & Interpretation Question Type 1: Finding the Tangent and Normal to a Polynomial at a Specific Value of x Exercises

Find the equations of the tangent and the normal to the curve $y=4x^3+x^2-2x+6$ at $x=0$. [6 marks]

Find the equations of the tangent and the normal to the curve $y=-x^4+2x^2-x+3$ at $x=1$.

Find the equations of the tangent and the normal to the curve $y=x^3-6x^2+4x+5$ at $x=4$.

Find the equations of the tangent and the normal to the curve $y=x^6-3x^3+2$ at $x=1$.

Find the equations of the tangent and the normal to the curve $y=-2x^3+4x+1$ at $x=-1$.

Find the equations of the tangent and the normal to the curve $y=x^2-3x+2$ at $x=1$.

Find the equations of the tangent and the normal to the curve $y=7x^3-x^2+2$ at $x=\frac{1}{2}$.

Find the equations of the tangent and the normal to the curve $y=5x^3+8x^2+9x+3$ at $x=5$.

Find the equations of the tangent and the normal to the curve $y=\frac{1}{2}{x}^2+3x-4$ at $x=-2$.

Find the equations of the tangent and the normal to the curve $y=3x^4-x^2+7$ at the point where $x=0$.

Find the equations of the tangent and the normal to the curve $y=2x^5-x^3+3x$ at $x=2$.

Find the equations of the tangent and the normal to the curve $y=-x^5+5x^3-x$ at $x=-2$.